A323073 Number of iterations of A049820(x) = x - A000005(x) needed to reach either zero or such x that x and A049820(x) are coprime, when starting from x = n.

0, 0, 1, 0, 0, 0, 2, 0, 1, 3, 3, 0, 3, 0, 4, 0, 0, 0, 4, 0, 5, 0, 5, 0, 1, 0, 6, 0, 6, 0, 6, 0, 7, 0, 7, 0, 1, 0, 8, 0, 8, 0, 8, 0, 9, 1, 9, 0, 9, 0, 10, 0, 10, 0, 10, 0, 10, 0, 11, 0, 10, 0, 12, 1, 0, 0, 12, 0, 13, 0, 13, 0, 11, 0, 14, 1, 14, 0, 14, 0, 14, 0, 15, 0, 12, 0, 16, 0, 15, 0, 15, 0, 17, 0, 16, 0, 13, 0

Offset: 0

Author

Antti Karttunen, Jan 05 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..110880

Crossrefs

Cf. A000005, A009191, A049820, A155043, A259934, A286540, A320009, A322974, A322987, A322996.

Cf. A046642 (positions of zeros after the initial a(0)=0).

Programs

PARI

A323073(n) = if(!n,0,my(nn=(n-numdiv(n))); if(1==gcd(n,nn),0,1+A323073(nn)));

PARI

A323073(n) = if(!n,0,for(j=0,oo,my(nn=(n-numdiv(n))); if((0==nn)||(1==gcd(n,nn)),return(j+(2==n)),n = nn)));

Formula

a(0) = 0; for n > 0, if A009191(n) == 1, a(n) = 0, otherwise a(n) = 1 + a(n-A000005(n)).

a(n) <= A155043(n).